Automatizacion de Sistemas de Manufactura Sesion 3 PLC Horner
Horner
8
Métodos de Horner + Newton-Raphson
-
Upload
geartu -
Category
Technology
-
view
33.290 -
download
0
description
Transcript of Horner
![Page 1: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/1.jpg)
Métodos de Horner
+ Newton-Raphson
![Page 2: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/2.jpg)
Forma de un polinomio
![Page 3: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/3.jpg)
Teorema fundamental del álgebra
Si P(x) es un polinomio de grado n >= 1con coeficientes reales o complejos,
entonces P(x) = 0 tiene al menos una raíz
![Page 4: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/4.jpg)
CorolarioSi P(x) es un polinomio de grado n >= 1 con coeficientes
reales o complejos, entonces existenúnicas x1, x2, ..., xk, posiblemente complejas, t enteros
positivos m1, m2, ..., mk tales que
y
![Page 5: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/5.jpg)
Método de Horner
![Page 6: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/6.jpg)
EjemploP(x) = 2x4 - 3x2 + 3x -4x0 = -2 División Sintética
Por tanto,
![Page 7: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/7.jpg)
P(x) = 2x4 - 3x2 + 3x -4
y
(Newton-Raphson)
![Page 8: Horner](https://reader036.fdocuments.co/reader036/viewer/2022082512/54c4c02f4a79598b2d8b462e/html5/thumbnails/8.jpg)
Algoritmo Horner